# What is a Matrix

A matrix can be thought of as an array of numbers. It is usually denoted by a capital letter (such as M), and each component (called an entry) can be denoted $ M_{ij} $ where i is the row number (starting from 1) and j is the column number (starting from 1). A matrix can have any number of rows and columns, depending on the context. When referring to an arbitrary matrix of a given size i rows by j columns it can be denoted $ M_{ixj} $

For example, the following is a 2x3 matrix: $ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} $

A matrix can be used to

- represent coefficients for a system of linear equations
- represent a linear transformation
- represent a basis of vectors
- represent information where matrix multiplication has a meaning attached (Examples include a permutation matrix and an adjacency matrix)